Exploring Mechanisms of Neural Robustness: Linking Geometry and Spectrum for Reliable Artificial Intelligence

Temel Kavramlar

Unsupervised local learning models with winner-take-all dynamics learn power law representations, which are indicative of a balanced trade-off between accuracy and robustness in neural representations.

Özet

The paper explores the interplay between the geometry, spectral properties, robustness, and expressivity of neural representations. It examines the link between representation smoothness and spectrum by using weight, Jacobian, and spectral regularization while assessing performance and adversarial robustness.
The key findings are:

Krotov and Hopfield's local learning model yields latent representations that are smooth and exhibit a power law spectrum, outperforming end-to-end backpropagation trained models in terms of robustness.

Weight regularization, particularly L2 and Jacobian regularization, also leads to smoother representations and improved robustness compared to the naive model, though they do not exhibit a clear power law spectrum.

Directly optimizing for a power law spectrum through spectral regularization does not seem sufficient to achieve the desired balance between accuracy and robustness.

The power law spectrum in the local learning model generalizes to arbitrary inputs, unlike the spectrally regularized model, suggesting the former captures more fundamental mechanisms.

The insights gained may elucidate the mechanisms that realize robust neural networks in mammalian brains and inform the development of more stable and reliable artificial systems.

İstatistikler

"Backpropagation-optimized artificial neural networks, while precise, lack robustness, leading to unforeseen behaviors that affect their safety."
"Recent work suggests power law covariance spectra, which were observed studying the primary visual cortex of mice, to be indicative of a balanced trade-off between accuracy and robustness in representations."
"Krotov and Hopfield's learning rule is directly related to the physiological learning processes, and its representations exhibit a power law spectrum."

Alıntılar

"Unlike artificial models, biological neurons adjust connectivity based on neighboring cell activity."
"Representations on smoother manifolds are less affected by small perturbations in the input which makes them less prone."
"An optimal balance between accuracy and robustness is characterized by a close to n^-α power law decay in ordered spectral components, where α depends on the input's intrinsic dimension."

Önemli Bilgiler Şuradan Elde Edildi

Exploring mechanisms of Neural Robustness: probing the bridge between geometry and spectrum

by Kons... : arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.00679.pdf

Daha Derin Sorular

What other biological mechanisms beyond local learning could be leveraged to achieve robust and reliable artificial neural networks

One biological mechanism beyond local learning that could be leveraged to achieve robust and reliable artificial neural networks is synaptic plasticity. Synaptic plasticity refers to the ability of synapses to strengthen or weaken over time based on neural activity. By incorporating principles of synaptic plasticity into artificial neural networks, models can adapt and learn from their environment in a more dynamic and flexible manner. This adaptability can enhance the network's robustness by allowing it to adjust to changing conditions and optimize its performance based on feedback.

How can the insights from the power law spectrum be extended to more complex neural network architectures beyond simple multi-layer perceptrons

The insights from the power law spectrum can be extended to more complex neural network architectures, such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs), by incorporating regularization techniques that promote smoothness and power law behavior in the representations learned by these models. For CNNs, this could involve applying spectral regularization to the convolutional layers to encourage power law spectra in the feature maps. Similarly, for RNNs, techniques like weight regularization or Jacobian regularization can be used to enforce smoothness in the hidden states and promote power law behavior in the spectral components. By integrating these principles into more complex architectures, researchers can potentially improve the robustness and generalization capabilities of deep learning models across various domains.

Can the principles of optimal representation smoothness and power law spectra be applied to improve the robustness of deep learning models in real-world applications

The principles of optimal representation smoothness and power law spectra can be applied to improve the robustness of deep learning models in real-world applications by guiding the design and training of these models. By optimizing neural networks to exhibit power law spectra in their representations, researchers can potentially enhance the models' ability to generalize to unseen data and resist adversarial attacks. Additionally, promoting smoothness in the learned representations can help reduce overfitting and improve the models' performance on diverse datasets. By incorporating these principles into the regularization and optimization processes of deep learning models, practitioners can develop more reliable and robust systems for real-world applications in areas such as image recognition, natural language processing, and autonomous driving.